The Explicitly Quasi-linear Relation Between the Order Parameter and Normalized Birefringence of Aligned Uniaxially Anisotropic Molecules Determined Using a Numerical Method

The birefringence of distributed, uniaxially anisotropic molecules like liquid crystals is calculated as the degree of ordering is varied. The relation between the normalized birefringence   and the orientational order parameter  is investigated. The distribution function, which enables one to monitor the degree of ordering of liquid crystals including randomly distributed ones, is introduced. Using this distribution function, a series of distributed liquid crystals with order parameters ranging from 0 to 1 are generated, and   and  of the correspondingly distributed liquid crystals are calculated. Based on the calculated data, it is revealed that   and  satisfy the quasi-linear relation of       , where  can be approximated as      . The anisotropy of molecular polarizability is also calculated, using the birefringence, and separately following Vuks’ method and Neugebauer’s method, and it is shown that the relations between  and the molecular-polarizability anisotropy are also quasi-linear.